The cost of an item is (12x+30) rupees and it must be less than (150) rupees. What is the solution for (x)?

Correct answer: (x<10)

The direct answer is option B: \(x<10\). “Less than 150” means a strict inequality, so write \(12x+30<150\). Subtract 30: \(12x<120\). Divide by positive 12: \(x<10\). Option A, \(x<12\), results from incorrect arithmetic or ignoring the constant term. Option B is correct and does not include 10; at \(x=10\), the cost is \(12(10)+30=150\), but the price must be less than 150. Option C uses \(\le\), which would mean “at most” and would allow 10. Option D reverses the direction and describes values greater than 10. In word problems, translate “less than” as < and “at most” as ≤.